Inconsistency of the ring-current model for the cyclopropenyl cation

We present results of a quantum-mechanical calculation of electron current density, magnetic susceptibility and proton magnetic shielding in the cyclopropenyl cation, reflecting on the ring-current model. The current density induced in and out of the molecular plane by a perpendicular magnetic field is plotted, showing the existence of localized distributions and paramagnetic circulations around the centre of the molecule.     

Comparison results for some types of relaxation of variational integral functionals

A comparison between some relaxation methods of an integral functional is carried out. The following relaxed functionals of the variational integral I(, u)= :

Electrochemical behavior of LiCoO2 as aqueous lithium-ion battery electrodes

Despite the large number of studies on the behavior of LiCoO₂ in organic electrolytes and its recent application as a positive electrode in rechargeable water battery prototypes, a little information is available about the lithium intercalation reaction in this layered compound in aqueous electrolytes. This work shows that LiCoO₂ electrodes can be reversibly cycled in LiNO₃ aqueous electrolytes for tens of cycles at remarkably high rates with impressive values specific capacity higher than 100 mAh/g, and with a coulomb efficiency greater than 99.7%. Stable and reproducible cycling measurements have been made using a simple cell design that can be easily applied to the study of other intercalation materials, assuming that they are stable in water and that their intercalation potential range matches the electrochemical stability window of the aqueous electrolyte. The experimental arrangement uses a three-electrode flooded cell in which another insertion compound acts as a reversible source and sink of lithium ions, i.e., as the counter electrode. A commercial reference electrode is also present. Both the working and the counter electrodes have been prepared as thin layers on a metallic substrate using the procedures typical for the study of electrodes for lithium-ion batteries in organic solvent electrolytes.     

Coloring linear orders with Rado's partial order

Let ?_R be the preorder of embeddability between countable linear orders colored with elements of Rado's partial order (a standard example of a wqo which is not a bqo). We show that ?_R has fairly high complexity with respect to Borel reducibility (e.g. if P is a Borel preorder, then P ≤_B ?_R), although its exact classification remains open. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the synthesis of vinyl and phenyl C-furanosides by stereospecific debenzylative cycloetherification

Open-chain benzyl-ether-protected polyols in which one of the alcohols is either allylic or benzylic are synthesised by addition of organometallic vinyl or phenyl reagents to benzyl-ether-protected carbohydrate hemiacetals. The diastereoselectivity of addition is dependent on whether a Grignard reagent or a trialkylzincate reagent is used. The open-chain compounds undergo a stereospecific cyclisation reaction on treatment with catalytic strong Brønsted acid with heating to form tetrahydrofurans with inversion of configuration at the allylic or benzylic carbon (C-1) and loss of hydroxyl from this position. A short synthesis of the starting material, 1,2,4,6-tetra-O-benzyl-d-galactose, from lactose is described.